Invariant meromorphic functions on Stein spaces

Fonctions méromorphes invariantes sur les espaces de Stein

Daniel Greb , Christian Miebach (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

In this paper we develop fundamental tools and methods to study meromorphic functions in an equivariant setup. As our main result we construct quotients of Rosenlicht-type for Stein spaces acted upon holomorphically by complex-reductive Lie groups and their algebraic subgroups. In particular, we show that in this setup invariant meromorphic functions separate orbits in general position. Applications to almost homogeneous spaces and principal orbit types are given. Furthermore, we use the main result to investigate the relation between holomorphic and meromorphic invariants for reductive group actions. As one important step in our proof we obtain a weak equivariant analogue of Narasimhan's embedding theorem for Stein spaces.

Mots clés: Lie group action; Stein space; invariant meromorphic function; Rosenlicht quotie

Domaines: Variables complexes [math.CV]

Daniel Greb, Christian Miebach. Invariant meromorphic functions on Stein spaces. Annales de l'Institut Fourier, 2012, 62 (5), pp.1983-2011. ⟨10.5802/aif.2740⟩. ⟨hal-03600367⟩